
0=fQ(Q0){ Q02+1r2+e-b[a2+(a4+12r)(a-b)]}
 .

One immediately finds that, from the second equation,
\(f_{Q}\left(Q_{0}\right)\)  and \(f(Q_{0})\)  must be vanished.
Such strict restrictions imply that a general functional form of \(f(Q)\)  should be
\(f(Q)=\underset{n}{\sum }a_{n}\left(Q-Q_{0}\right)^{n}\) .
Therewith one could construct specific models of cosmological interest,
for instance DE models of polynomial form

f(Q)=Q+nQ0[1-(QQ0)1/n]-Q0
 ,

and of exponential form

f(Q)=Q-nQ0{ 1-[1-(QQ0)1/n]} -Q0
 .


Other variants of the above models could be those of arctangent form

f(Q)=Q+nQo[1-(QQ0)1/n]-Q0
 ,


and of logarithmic form

f(Q)=Q+nQ0{ 1-[1+(QQ0)]1/n} -Q0
 .


Our models are similar to the well known DE models in \(f(R)\)  gravity [1]}, moreover, all of them satisfy the stabilization conditions, i.e., \(f_{Q}>0\)  and \(f_{QQ}>0\) .
Furthermore, our polynomial model can be reduced to the models proposed in Ref. [2]} with particular parameter choices except for a constant difference.
And one of the advantages of our model is that it has only one undetermined parameter \(n\)  due to the strong constraints on \(f(Q)\) 
Cosmological applications of these models are out of the scope of the current work,
so we shall leave it for future work.
